4-4 the slope formulathe slope formula
TRANSCRIPT
Holt McDougal Algebra 1
4-4 The Slope Formula4-4The Slope Formula
Holt Algebra 1
Lesson Quiz
Lesson Presentation
Warm Up
Holt McDougal Algebra 1
Holt McDougal Algebra 1
4-4 The Slope Formula
Warm Up
Add or subtract.
1. 4 + (–6) 2. –3 + 5
3. –7 – 7 4. 2 – (–1)
Find the x- and y-intercepts.
5. x + 2y = 8
6. 3x + 5y = –15 x-intercept: –5; y-intercept: –3
x-intercept: 8; y-intercept: 4
–2 2
3–14
Holt McDougal Algebra 1
4-4 The Slope Formula
Find slope by using the slope formula.
Objective
Holt McDougal Algebra 1
4-4 The Slope Formula
In Lesson 5-3, slope was described as the constant rate of change of a line. You saw how to find the slope of a line by using its graph.
There is also a formula you can use to find the slope of a line, which is usually represented by the letter m. To use this formula, you need the coordinates of two different points on the line.
Holt McDougal Algebra 1
4-4 The Slope Formula
Holt McDougal Algebra 1
4-4 The Slope Formula
Example 1: Finding Slope by Using the Slope Formula
Find the slope of the line that contains (2, 5) and (8, 1).
Use the slope formula.
Substitute (2, 5) for (x1, y1) and
(8, 1) for (x2, y2).
Simplify.
The slope of the line that contains (2, 5) and (8, 1)
is .
Holt McDougal Algebra 1
4-4 The Slope Formula
Find the slope of the line that contains (–2, –2) and (7, –2).
Check It Out! Example 1a
Use the slope formula.
Substitute (–2, –2) for (x1, y1) and
(7, –2) for (x2, y2).
Simplify.
The slope of the line that contains (–2, –2) and (7, –2) is 0.
= 0
Holt McDougal Algebra 1
4-4 The Slope Formula
Find the slope of the line that contains (5, –7) and (6, –4).
Check It Out! Example 1b
Use the slope formula.
Substitute (5, –7) for (x1, y1) and
(6, –4) for (x2, y2).
Simplify.
The slope of the line that contains (5, –7) and (6, –4) is 3.
= 3
Holt McDougal Algebra 1
4-4 The Slope Formula
Find the slope of the line that contains
and
Check It Out! Example 1c
Use the slope formula.
Substitute for (x1, y1)
and for (x2, y2) and
simplify.
The slope of the line that contains and
is 2.
Holt McDougal Algebra 1
4-4 The Slope Formula
Sometimes you are not given two points to use in the formula. You might have to choose two points from a graph or a table.
Holt McDougal Algebra 1
4-4 The Slope Formula
Example 2A: Finding Slope from Graphs and Tables
The graph shows a linear relationship. Find the slope.
Let (0, 2) be (x1, y1) and (–2, –2) be (x2, y2).
Simplify.
Use the slope formula.
Substitute (0, 2) for (x1, y1)
and (–2, –2) for (x2, y2).
Holt McDougal Algebra 1
4-4 The Slope Formula
Example 2B: Finding Slope from Graphs and Tables
The table shows a linear relationship. Find the slope.
Step 1 Choose any two points from the table. Let (0, 1) be (x1, y1) and (–2, 5) be (x2, y2).
Step 2 Use the slope formula.
The slope equals –2
Use the slope formula.
Substitute (0, 1) forand (–2, 5) for .
Simplify.
Holt McDougal Algebra 1
4-4 The Slope Formula
Check It Out! Example 2a
The graph shows a linear relationship. Find the slope.
Simplify.
Use the slope formula.
Let (4, 4) be (x1, y1) and (8, 6) be (x2, y2).
Substitute (4, 4) for (x1, y1)
and (8, 6) for (x2, y2).
Holt McDougal Algebra 1
4-4 The Slope Formula
Check It Out! Example 2b
Simplify.
Use the slope formula.
Let (–2, 4) be (x1, y1) and (0, –2) be (x2, y2).
Substitute (–2, 4) for (x1, y1)
and (0, –2) for (x2, y2).
The graph shows a linear relationship. Find the slope.
Holt McDougal Algebra 1
4-4 The Slope Formula
Check It Out! Example 2c
The table shows a linear relationship. Find the slope.
Step 1 Choose any two points from the table. Let (0, 1) be (x1, y1) and (2, 5) be (x2, y2).
Step 2 Use the slope formula.
Use the slope formula.
Simplify.
Substitute (0, 1) for (x1, y1)
and (2, 5) for (x2, y2).
Holt McDougal Algebra 1
4-4 The Slope Formula
Check It Out! Example 2d
The table shows a linear relationship. Find the slope.
Step 1 Choose any two points from the table. Let (0, 0) be (x1, y1) and (–2, 3) be (x2, y2).
Step 2 Use the slope formula.
Use the slope formula.
Simplify
Substitute (0, 0) for (x1, y1)
and (–2, 3) for (x2, y2).
Holt McDougal Algebra 1
4-4 The Slope Formula
Remember that slope is a rate of change. In real-world problems, finding the slope can give you information about how a quantity is changing.
Holt McDougal Algebra 1
4-4 The Slope Formula
Example 3: Application
The graph shows the average electricity costs (in dollars) for operating a refrigerator for several months. Find the slope of the line. Then tell what the slope represents.
Step 1 Use the slope formula.
Holt McDougal Algebra 1
4-4 The Slope Formula
Example 3 Continued
Step 2 Tell what the slope represents.
In this situation y represents the cost of electricity and x represents time.
So slope represents in units of
.
A slope of 6 mean the cost of running the refrigerator is a rate of 6 dollars per month.
Holt McDougal Algebra 1
4-4 The Slope Formula
Check It Out! Example 3
The graph shows the height of a plant over a period of days. Find the slope of the line. Then tell what the slope represents.
Step 1 Use the slope formula.
Holt McDougal Algebra 1
4-4 The Slope Formula
Check It Out! Example 3
Step 2 Tell what the slope represents.
In this situation y represents the height of the plant and x represents time.
So slope represents in units of
.
A slope of mean the plant grows at rate of 1
centimeter every two days.
Holt McDougal Algebra 1
4-4 The Slope Formula
If you know the equation that describes a line, you can find its slope by using any two ordered-pair solutions. It is often easiest to use the ordered pairs that contain the intercepts.
Holt McDougal Algebra 1
4-4 The Slope Formula
Example 4: Finding Slope from an Equation
Find the slope of the line described by 4x – 2y = 16.
Step 1 Find the x-intercept. Step 2 Find the y-intercept.
4x – 2y = 16
4x = 16
x = 4Step 3 The line contains (4, 0) and (0, –8). Use the
slope formula.
4x – 2y = 16
–2y = 16
y = –8
4x – 2(0) = 16 Let y = 0. 4(0) – 2y = 16 Let x = 0.
Holt McDougal Algebra 1
4-4 The Slope Formula
Check It Out! Example 4
Find the slope of the line described by 2x + 3y = 12.
Step 1 Find the x-intercept. Step 2 Find the y-intercept.
2x + 3y = 12 2x + 3y = 12
2x + 3(0) = 12 Let y = 0. 2(0) + 3y = 12 Let x = 0.
2x = 12
x = 6
3y = 12
y = 4
Step 3 The line contains (6, 0) and (0, 4). Use the
slope formula.
Holt McDougal Algebra 1
4-4 The Slope Formula
Lesson Quiz
1. Find the slope of the line that contains (5, 3)
and (–1, 4).
2. Find the slope of the line. Then tell what the slope represents.
50; speed of bus is 50 mi/h
3. Find the slope of the line described by x + 2y = 8.